An arbitrarily chosen interfacing device or load does not automatically comply with an input current source as illustrated in Fig. 3.1. The system in Fig. 3.1a consists of current source (subsystem S) and current-sink load (subsystem L) requiring that the input current iS and load current iL are equal in all circumstances. In practice, the input current is considered as constant but the current-sink load may be based on a controllable switching device causing a situation where iS ziL. Consequently, Kirchhoff’s current law is violated. The connection in Fig. 3.1b satisfies Kirchhoff’s current law since it consists of a dual pair of circuit elements, i.e. a current source connected to a voltage-type load. It can be concluded that a current source requires an interfacing device that resembles a voltage-type load.
Chapter 3 Implementation of Current-Fed Converters
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Fig. 3.1 a) Invalid and b) valid interfacing of a current source
Consider an implementation of a switched-mode battery charger fed by a constant current source. The input variables of the system are obviously the input current and output (battery) voltage and the output variables output (charge) current and input voltage. First, the physical power stage has to comply with the equivalent model shown in Fig. 3.2a; the input port must be a voltage-type load to satisfy Kirchhoff’s current law and the output port a current source to satisfy Kirchhoff’s voltage law. The capacitor is known to resist changes in the voltage, i.e. it resembles constant-voltage load when it is charged and voltage source when discharged. Similarly, the inductor is known to resist the changes in the current, i.e. it resembles current sink when it is charged and current source when discharged. Therefore, the power stage is based on the usage of an input capacitor C and output inductor L as shown in Fig. 3.2b.
Fig. 3.2 a) Equivalent model of a CF battery charger and b) the principle of an actual CF power stage
The basic current converters or regulators are based on stepping the current either up or down. If the input current is higher than the allowed charging current, the current must be stepped down naturally. Respectively, if the current source provides a rather low current, the step-up function is desired. The output voltage can be also seen to be reversely stepped up/down to the input terminal. This is possible because the input source is assumed to be constant current source of which voltage can be controlled and regulated.
3.2.1 Step-Down Current Regulator
In order to step down the charge current, the current regulation has to be arranged in such way that it chops the input current. This can be implemented by the switching structure shown in Fig. 3.3a. Basically, the switch S is chopping the input current and the
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current ripple is filtered by the CL-filter. In position 1 (Fig. 3.3b), the switch provides a current path from input to output. When the switch is changed to position 2 (Fig. 3.3c), the input current source is short-circuited and the charge current is maintained by the CL structure.
Fig. 3.3 a) Step-down current regulator, b) sub-circuit when the switch is in position 1 and b) position 2
The small-ripple approximated currents and voltages at different switch positions are as follows:
in-1 C
o-1 L
L-1 C o in o
C-1 in L in o
u U
i I
u U U U U
i I I I I
in-2
o-2 L
L-2 C o
C-2 L o
0 u i I
u U U
i I I
where switch position 1 is denoted by subscript ‘-1’ and position 2 by subscript ‘-2’.
The relations between the input variables and output variables can be solved by applying ampere-second balance for the capacitor over one switching period [91]:
1 1
1 1
C-1 C-2 in o o
0TS C( ) 0t TS 0t( ) TS 0
t t
i t dt i dt i dt I I dt I dt
³ ³ ³ ³ ³
(3.1)where TS is the switching period and t1 the time the switch is in position 1. This time interval can be expressed by using certain duty ratio D yielding t1 DTS. Consequently, the output current can be solved from (3.1) as a function of the input current and duty ratio yielding
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o in
I DI , (3.2)
If the losses are neglected, the input power equals the output power (i.e.
in in in o o o
P U I P U I ) and the input voltage can be given as follows:
in o
U DU . (3.3)
Since the duty ratio D is always equal to or less than one, the step-down function of the current is obvious according to (3.2) and analogous to conventional VF buck converter which steps down the voltage instead. Therefore, the converter under study is known as dual buck or CF buck converter [78],[P4].
3.2.2 Step-Up Current Regulator
In order to step up the current, the current regulation has to be arranged in such a way that it accumulates the charge current. This can be implemented by the switching structure shown in Fig. 3.4a. When switch S is in position 1 (Fig. 3.4b) the capacitor is charged by the input current source and charge current is maintained by the output inductor. When the switch is changed into position 2 (Fig. 3.4c) the charge current is accumulated because it is a sum of input current and capacitor discharge current.
Fig. 3.4 a) Step-up current regulator, b) sub-circuit when the switch is in position 1 and b) position 2
The small-signal approximated currents and voltages at different switch positions are as follows:
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26
in-1 C
o-1 L
L-1 o
C-1 in
u U
i I
u U
i I
in-2 C
o-2 L
L-2 C o in o
C-2 in L in o
u U
i I
u U U U U
i I I I I
where switch position 1 is denoted by subscript ‘-1’ and position 2 by subscript ‘-2’.
The ampere-second balance for the capacitor is as follows [91]:
1 1
1 1
C-1 C-2 in in o
0TS C( ) 0t TS 0t TS( ) 0
t t
i t dt i dt i dt I dt I I dt
³ ³ ³ ³ ³
(3.4)where TS is the switching period and t1 the time switch is in position 1. This time interval can be expressed by using duty ratio D yielding t1 DTS. Consequently, the output current can be solved from (3.4) as a function of the input current and duty ratio yielding
in o
I I
Dc, (3.5)
where Dc 1 D, i.e. the complement of the duty ratio. If the losses are neglected, the input voltage can be given as follows:
o in
U U
Dc. (3.6)
Since term (1 /Dc) is always equal to or more than one, the current-boosting nature of the converter is obvious according to (3.5) and is analogous to conventional VF boost converter, which steps up voltage instead. Therefore, the converter is known in literature as the dual boost or CF boost converter [78],[P7].